Geodesic
Closed Submodules of Holomorphic Functions with Two Generators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 65-80

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Let $I$ be a closed submodule over a polynomial ring in a space of holomorphic functions on a domain in the complex plane. We establish sufficient conditions under which $I$ is generated by two functions or two special submodules. As a corollary, it follows from these results that if an invariant subspace $W\subset C^{\infty}(a,b)$ (with respect to the differentiation operator) admits spectral synthesis, then it is the solution space of a system of two homogeneous convolution equations.
Keywords: spaces of holomorphic functions, module over the ring of polynomials, local description of closed submodules, finitely generated submodule, spectral synthesis
Mots-clés : convolution equation. 
@article{FAA_2004_38_1_a5,
     author = {B. N. Khabibullin},
     title = {Closed {Submodules} of {Holomorphic} {Functions} with {Two} {Generators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {65--80},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_1_a5/}
}
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B. N. Khabibullin. Closed Submodules of Holomorphic Functions with Two Generators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 65-80. http://geodesic.mathdoc.fr/item/FAA_2004_38_1_a5/